Diffusion weighted imaging (DWI) in MRI can probe microstructure of the tissue. It not only provides structural but also functional information, thus it has tremendous potentials in application of the clinical and neuroimaging. However, at the current moment diffusion imaging uses single shot acquisition method to suppress motion artifacts, which inevitably has low spatial resolution, low signal to noise ratio (SNR) and image distortion artifacts. With the increasing demand in the clinical and neuroscience research, diffusion weighted images are expected to provide high resolution and high SNR. For traditional MRI, however, it is always a challenge to improve spatial resolution and SNR while keeping the scan time relatively short.
With the recent introduction of parallel imaging, the acquisition time can be reduced while image resolution can be improved. Parallel imaging makes full use of the distinct sensitivities of individual element of multiple-channel coils that allow one to sample k-space more sparsely and thus more quickly. The acceleration of k-space traveling along the phase encoding direction is controlled by the reduction factor, R, which is the ratio between the number of full phase-encoding lines and that of undersampling lines. However, parallel imaging scans come with a SNR penalty that is proportional to square root of R plus an extra geometry-related factor. For that restriction, R not larger than 2 is usually adopted in practice. Up to now, there are no reliable imaging and reconstruction methods established yet for preserving SNR while reducing acquisition time simultaneously.